Overview Divide Fractions
LESSON 10Overview Divide FractionsSTANDARDS FOR MATHEMATICALPRACTICE (SMP)ObjectivesPrior KnowledgeSMP 1, 2, 3, 4, 5, and 6 are integrated into theTry-Discuss-Connect routine.*Content Objectives This lesson provides additional support for:1 Make sense of problems and persevere insolving them.7 Look for and make use of structure.* See page 1q to learn how every lesson includesthese SMP. Divide fractions by fractions using visualmodels and equations.Use visual models and equations torepresent word problems involvingfraction division.Interpret the quotient of two fractions.Solve fraction division problems, including those that have quotientsthat are fractions.Write a word problem to match a givenexpression involving division of fractions.Language Objectives Discuss connections between visualmodels and equations in word problemsinvolving fraction division with a partner.Read and interpret word problems todetermine which quantity is the dividendand which quantity is the divisor.Justify the size of the quotient in relationship to the dividend and divisorusing reasoning and understanding offraction division in class discussion.Apply understanding of division withfractions to write a word problem tomatch a given expression using completesentences.Understand and use lesson vocabulary toaccurately explain division of fractions. Understand that a divisor can representthe size of a group or the number ofgroups.Add, subtract, and multiply fractions.Interpret a fraction as division.Use visual models to represent divisionwith fractions.Write a mixed number as a fractiongreater than 1.VocabularyMath Vocabularyreciprocal for any nonzero number a,the reciprocal is 1 . The reciprocal of anya··fraction a is b . Zero does not have ab·· reciprocal.a··Review the following key terms.common denominator a number that is acommon multiple of the denominators oftwo or more fractions.fraction a number that names equal partsof a whole. A fraction names a point on thenumber line and can also represent thedivision of two numbers.Academic Vocabularynonzero not equal to zero.Learning ProgressionIn Grade 5, students multipliedfractions by whole numbers and otherfractions. They also divided wholenumbers by unit fractions and unitfractions by whole numbers.In the previous lesson, students usedvisual models, including bar models andnumber lines, to find a quotient of twofractions when the fractions werecompatible and when the quotient wasa whole number.207aLESSON 10 Divide FractionsIn this lesson, students use models andstrategies to divide fractions, includingmixed numbers. They look at situationsin which the quotient is not a wholenumber, including when the divisor is awhole number or a fraction. When thereis a remainder, they understand how towrite the remainder as a fraction of thedivisor. Students explore an algorithmfor dividing fractions—multiplying bythe reciprocal of the divisor—and theyunderstand why this algorithm works.They solve a variety of word problemsinvolving division of fractions.In the next lesson, students build ontheir skills and understandings ofmultiplying and dividing fractions asthey solve volume problems for prismswith fractional edge lengths.In Grade 7, students will extend theirwork with fractions to performoperations with positive and negativerational numbers. Curriculum Associates, LLCCopying is not permitted.
LESSON 10OverviewPacing GuideItems marked withSESSION 1 are available on the Teacher Toolbox.MATERIALSDIFFERENTIATIONExplore Dividing Fractions (35–50 min)Start (5 min) Try It (5–10 min )Discuss It (10–15 min)Connect It (10–15 min)Close: Exit Ticket (5 min)Math Toolkit fraction bars, fractioncircles, grid paper, number linesPresentation SlidesPREPARE Interactive TutorialRETEACH or REINFORCE Hands-On ActivityMaterials For each pair: 1 set of fraction tilesAdditional Practice (pages 211–212)SESSION 2 Develop Interpreting a Remainder When the Divisor Is a Fraction (45–60 min)Start (5 min) Try It (10–15 min )Discuss It (10–15 min)Connect It (15–20 min)Close: Exit Ticket (5 min)Math Toolkit fraction bars, fractioncircles, grid paper, number linesPresentation SlidesRETEACH or REINFORCE Hands-On ActivityMaterials For each pair: 13 connecting cubesREINFORCE Fluency & Skills PracticeEXTEND Deepen UnderstandingAdditional Practice (pages 217–218)SESSION 3 Develop Dividing by a Fraction (45–60 min)Start (5 min) Try It (10–15 min )Discuss It (10–15 min)Connect It (15–20 min)Close: Exit Ticket (5 min)Math Toolkit fraction bars, fractioncircles, grid paper, number linesPresentation SlidesRETEACH or REINFORCE Hands-On ActivityMaterials For each pair: 2 sets of fraction circlesREINFORCE Fluency & Skills PracticeEXTEND Deepen UnderstandingAdditional Practice (pages 223–224)SESSION 4 Refine Dividing Fractions (45–60 min)Start (5 min) Monitor & Guide (15–20 min )Group & Differentiate (20–30 min)Close: Exit Ticket (5 min)Math Toolkit Have items fromprevious sessions available forstudents.Presentation SlidesRETEACH Hands-On ActivityMaterials For each group: 7 sets of fractioncirclesREINFORCE Problems 4–8EXTEND ChallengePERSONALIZELesson 10 Quiz orDigital Comprehension CheckRETEACH Tools for InstructionREINFORCE Math Center ActivityEXTEND Enrichment Activity Curriculum Associates, LLCCopying is not permitted.LESSON 10 Divide Fractions207b
LESSON 10Overview Divide FractionsConnect to Culture Use these activities to connect with and leverage the diverse backgroundsand experiences of all students. Engage students in sharing what theyknow about contexts before you add the information given here.SESSION 1Try ItAsk students if they have ever made anything out of ceramic pottery clay orpolymer modeling clay. Clay can be used to make a variety of things, such as bricks,tiles, dishware, pots, sculptures, and even toys. Once a figure is formed, dependingon the type of clay, it can be air dried, baked, or fired in a kiln at very hightemperatures to become hard. Ask students to share objects they have seen or usedthat are made from clay.SESSION 2Try ItJuneteenth is a celebration of the ending of slavery in the United States.On June 19th, 1865, news of Lincoln’s Emancipation Proclamation finally reachedTexas, two and a half years after slaves were officially freed. Now, some people makea journey back to Galveston, Texas to celebrate Juneteenth. Sporting events,barbecues, and guest speakers have become important parts of the tradition. Thenumber of cities and states that celebrate Juneteenth continues to grow to this day.Survey students to determine if they know of or have participated in any othercelebrations of freedom.SESSION 3Try ItChicken feed is the food given to chickens. Different feed is used foryounger chickens versus older ones: starter feed for babies, grower feed for youngchickens, and various types of feed for adults. There are different forms and differentingredients of chicken feed. Depending on the role of the chicken—for example,laying eggs—there should be a different mix of mash, pellets, shell grit, and chickenscratch for a good meal. Have students describe different varieties of food they haveseen or know of for other animals.JuneteenthFestivalfeaturing3 2 Hours ofrmancesPerfofeaturing1SESSION 4Apply It Problem 5 Tomatoes are a popular plant for many gardeners. There aremany different types of tomatoes. Tomatoes are commonly red, but there are alsoorange, yellow, purple, and black tomatoes. Tomatoes can be small like grapes or aslarge as melons. They are typically grown in soil, but some farmers choose to useonly water and nutrients instead. Have students discuss different dishes that includetomatoes as an ingredient.207cLESSON 10 Divide FractionsC E L E B R AT I N G F R E E D O M Curriculum Associates, LLCCopying is not permitted.
LESSON 10OverviewConnect to Family and Community After the Explore session, have students use the Family Letter to let theirfamilies know what they are learning and to encourage family involvement.LESSON 10 DIVIDE FRACTIONSActivity Thinking AboutFraction Division Around YouLESSON10This week your student is learning how to divide fractions.When dividing fractions, it is helpful to think about the relationship betweenmultiplication and division. Just as the equations 2 3 4 5 8 and 8 4 4 5 2 tell youthere are two 4s in 8, the equations below tell you there is only half of 14 in 18 our student will be learning to solve problems like the one below. Do this activity together to investigate divisionwith fractions in the real world.Divide FractionsDear Family,Cities and towns often have rules for how land isused for housing. A town might require that a group of townhousesis built on at least 1 12 acres of land. The town might also require that each··townhouse in the group has 1 acre of land.6··The division expression 1 1 4 1 tells how many 1 -acre lots fit into 1 1 acres of2662········land. Because 1 1 4 1 5 9, a builder knows that 9 townhouses can be built on26····1 1 acres of land.2··A recipe calls for 1 1 cups of rice. You only have a 1 -cup measure.23····How many scoops of the 1 -cup measure should you use?What would the division expression be if the2acres and each house needs 41 acre?builder has 5··3··3·· ONE WAY to find how many ··13s are in 1 ··12 is to use the common denominator 6.Split 1 whole into parts of size 1 . Now you can see that 1 1 5 9 and 1 5 2 .2··6··6··3··6··125 63161616161616There are 4 full groups of 13··plus 1 of a group of 1 .2··9112 5 63··11 4 1 5 9 2 5 412··3··6··6··2·· ANOTHER WAY is to use multiplication.Multiply 1 1 by 3 to find how many 1s are in 1 1 wholes.232······11 4 1 5 11 3 32··3··2··The numbers 1 and 3 are called reciprocals.3··5 3 332··5 9 , or 4 12··2··Using either method, you need 4 1 scoops of the2··1 -cup measure to have 1 1 cups of rice.32····Use the next page to start aconversation about fraction division.LESSON 10 Divide Fractions Curriculum Associates, LLC Copying is not permitted.207208LESSON 10 Divide Fractions Curriculum Associates, LLC Copying is not permitted.Connect to Language For English language learners, use the Differentiation chart to scaffold thelanguage in each session. Use the Academic Vocabulary routine for academicterms before Session 1.DIFFERENTIATION ENGLISH LANGUAGE LEARNERSMATH TERMTo estimatemeans to givean approximatenumber oranswer basedon mathematicalthinking.ACADEMICVOCABULARYA portion is apart of a largeramount. Curriculum Associates, LLCUse with Session 1Connect ItLevels 1–3: Reading/ListeningLevels 2–4: Reading/ListeningLevels 3–5: Reading/ListeningSupport students as they interpretConnect It problem 2. Read theproblem aloud. Display and clarify theMath Term and Academic Vocabulary.Guide students to make sense of theproblem by sketching the examplesprovided in parts a and b and askingstudents to make observations aboutthe sketches. Call on volunteers to helpyou label the quotient and dividend ineach sketch. Have students turn andtalk about each example using thephrases greater than or less than.Call on volunteers to share answersand explain their thinking. Reword asneeded to model precise languageand clarify ideas.Support students as they interpretConnect It problem 2. Read theproblem with students. Have studentsturn and talk to define estimate. Displaythe definition provided and havestudents revise and improve theirdefinitions based on the one provided.Repeat for portion.Allow time for partners to make senseof parts a and b by sketching theexamples provided in each part. Reviewthe sentence frames and ask partnersto decide which to use for parts a and b: The quotient is greater than thedividend . The quotient is less than thedividend .Support students as they interpretConnect It problem 2. Read theproblem with students. Have themtalk with a partner to develop adefinition for estimate. Display thedefinition provided. Adapt Say ItAnother Way by recording differentways that partners state the meaningof the term. Repeat for portion.Begin a Co-Constructed WordBank of terms that might be usedto talk and write about the problem.Students are likely to suggest quotient,dividend, greater than, and less than.You might add estimate and portion.Encourage students to use the termsas they respond to the problem.Copying is not permitted.LESSON 10 Divide Fractions207–208
LESSON 10 SESSION 1Explore Dividing FractionsPurpose LESSON 10 SESSION 1Explore the idea that dividing a fraction by a wholenumber can be thought of as decomposing the fractioninto equal-size parts.Understand that when dividing by a fraction, thequotient is sometimes greater than the dividend.STARTExplore Dividing FractionsPreviously, you learned what it means to divide withfractions. In this lesson, you will learn more aboutdividing fractions.CONNECT TO PRIOR KNOWLEDGE Use what you know to try to solve the problem below.StartWhich One Doesn’t Belong? 2Ramona is making clay animals with her friends. She has 3 lb of clay. She shares the4··clay equally among herself and 3 friends. How much clay does each person have?2A BCTRYITMath Toolkit fraction bars, fractions circles, grid paper, number linesSAMPLE APossible work:14 lb Curriculum Associates, LLC Copying is permitted.There are 4 people, so each person getsPossible Solutions1 of each 1 lb of clay.4··1 of 1 5 1 3 1 5 1444416···········Each person has 3 lb of clay.16···A is the only expression written as a division expression.B is the only expression that is not equivalent to 3.3160 116WHY? Support students’ facility withrecognizing the connection between divisionand multiplication with fractions.SMP 2, 3, 6Support Partner DiscussionAfter students work on Try It, have them respond toDiscuss It with a partner. Listen for understanding of: drawing a model that represents 3 lb. dividing 3 into 4 equal parts.4··finding 1 of 3 .2094··4··LESSON 10 Divide Fractions4··3163161431624DISCUSS ITAsk: How does yourmodel show thatRamona shares theclay equally amongherself and 3 friends?1343 5 12 . When you divide 12 into 4 equal parts, each part is 3 .161616·········Each person has 3 lb of clay.16···Share: My modelshows . . .Learning TargetSMP 1, SMP 2, SMP 3, SMP 4, SMP 5, SMP 6, SMP 7Interpret and compute quotients of fractions, and solve word problems involving division offractions by fractions.Make Sense of the ProblemDISCUSS IT34 lb4··SMP 1, 2, 4, 5, 6See Connect to Culture to support studentengagement. Before students work on Try It, useSay It Another Way to help them make sense of theproblem. If students identify 3 as an importantquantity in the problem, have them reread the thirdsentence carefully and turn and talk to discuss whatthis means in terms of what the problem is asking.116SAMPLE BC is the only expression that does not include awhole number.TRY IT1 1 1 1 116 16 16 16 164··209LESSON 10 Divide Fractions Curriculum Associates, LLC Copying is not permitted.209Common Misconception Listen for students who divide the denominator of 4 in 3 4··by 4, giving a result of 3 instead of 3 . As students share their strategies, ask them to116····think about how they can use multiplication to check their answer. For example, havestudents write 3 3 4 to understand that the product would be 12, not 3 .1··4··Select and Sequence Student StrategiesSelect 2–3 samples that represent the range of student thinking in your classroom.Here is one possible order for class discussion: (misconception) expressions that divide only the denominator by 4 insteadof 3 4 4 4··bar models that show 3 fourths each divided into 4 equal partsarea models that show 3 divided into 4 equal parts4··number lines that show 4 equal jumps of 3 from 0 to 3 16··4··equations for conversion of 3 pound to 12 ounces and division by 44·· Curriculum Associates, LLCCopying is not permitted.
LESSON 10 SESSION 1ExploreFacilitate Whole Class DiscussionLESSON 10 SESSION 1Call on students to share selected strategies. Useturn and talk to help students reason through theirmodels before sharing with the group.CONNECT ITLook Back How much clay does each person have when Ramona shares herclay? Explain how you know.1After each strategy, allow individual think time forstudents to process the ideas. Encourage studentsto identify ideas they agree with and add details tobuild onto those ideas.3 lb; Possible explanation: You can divide 3 lb of clay into 4 equal parts by4··making 12 parts that are each 1 lb. 12 4 4 5 3, so each person has 3 lb.1616······16···Look Ahead Dividing ··34 lb of clay equally among several people is a division2ASK How does [student name]'s model showdivision?situation that involves fractions. As when you divide with whole numbers, it canbe helpful to estimate a quotient before you divide.LISTEN FOR Division is splitting a quantity intoequal groups to find the number or size of thegroups. Representations should show a quantity, 3 , divided into 4 equal groups.a. Estimate whether 3 4 6 is greater than or less than the dividend, 3 . Use an4··4··Less than 3 ; Possible explanation: Each portion will weigh less than 3 lb4··14··SMP 2, 4, 5b. Estimate whether 2 1 4 1 is greater than or less than the dividend, 2 1 . Use an2··4··2··4··Greater than 2 1 ; Possible explanation: Each pound of clay is made up ofmodels show the dividend as 12 equal partsthat are each 1 , the divisor as 4, and the16··quotient as 3 , or three 1 s.2··4 parts of size 1 lb, so the number of 1 -lb portions is at least 2 4, or 8.4··16··4··c. Yolanda estimates that 3 1 4 1 is about 24. Show how to use multiplication to4··DIFFERENTIATION RETEACH or REINFORCE24 1 5 24 18··3·· length of 2 one-third tiles is 2 .]3··Ask: In terms of fraction tiles, what does it meanto divide 2 by 4? [It means you have to find3··4 equal-size tiles that have the same total length asthe 2 one-third tiles set end-to-end.]Allow time for students to determine which sizefraction tile they can use 4 of to have the samelength as the 2 one-third tiles.Ask: Which fraction tile can you use 4 of to equalthe length of the 2 one-third tiles? 3 1 4 6··Ask: What is the quotient 2 4 4? 3 1 4 36····Have students repeat the activity for otherquotients of fractions and whole numbers, suchas 2 4 and 1 6. 3 1 ; 1 4 5··2·· Curriculum Associates, LLC8··3 is close to 3 1 , so the estimate of 24 is reasonable.4··If students are unsure about dividing a fraction by awhole number, then use this activity to help themmodel division of a fraction by a whole number.Ask: How does this model represent 2 ? [The total1···5 24 5 38··· Use fraction tiles to model a fractiondivided by a whole number.3··8··check whether Yolanda’s estimate is reasonable.Hands-On ActivityMaterials For each pair: 1 set of fraction tiles Explain to students that they will be modeling 2 4 4. Have students start with 2 one-third tiles.2··example of dividing 2 1 lb of clay into 1 -lb portions to explain your thinking.Look Back Look for understanding that the16··4··because you divide the 3 lb into 6 smaller pieces.4··CONNECT IT4··example of dividing 3 lb of clay into 6 equal portions to explain your thinking.Reflect What division equation can you write to show that when ··34 lb of clay is3divided equally among 6 people, each person gets 1 lb of clay? How would you8··use multiplication to check that the quotient is correct?3 4 6 5 1 ; Possible explanation: Check that the product 6 1 is 3 .88 ··4····4··2102102LESSON 10 Divide Fractions Curriculum Associates, LLC Copying is not permitted.Look Ahead Point out that the estimates in parts a and b help studentsrecognize whether the quotient is greater than or less than the dividend.Students should recognize the multiplicative relationship between the quotient,the divisor, and the dividend.CLOSE3EXIT TICKETReflect Look for understanding of writing an equation that correctlyshows the dividend, divisor, and quotient and that multiplying thequotient by the divisor can be used to check the equation.Common Misconception If students are unclear about where to write thedividend, divisor, and quotient in an equation, then have them write asentence to describe the situation and then substitute symbols for words.For example, students may write “ 34 divided equally among 6 people is 18 lb····each” and translate this to the equation 3 4 6 5 1 .4··8··10 ··12··Copying is not permitted.LESSON 10 Divide Fractions210
LESSON 10 SESSION 1Prepare for Dividing FractionsLESSON 10 SESSION 1Support VocabularyDevelopmentName:Prepare for Dividing FractionsAssign Prepare for Dividing Fractions as extrapractice in class or as homework.1If you have students complete this in class, then use theguidance below.Ask students to consider the term fraction and toconsider the parts of a fraction. Review that thenumerator tells the number of equal parts that aredescribed and the denominator tells the number ofequal parts that are in the whole.Think about what you know about fractions. Fill in each box. Use words, numbers,and pictures. Show as many ideas as you can.Possible answers:What Is It?What I Know About Ita number that names equal partsof a wholeThe numerator tells you the number ofequal parts there are.The denominator tells you the number ofequal parts in the whole.A fraction can represent the division oftwo numbers.Have students work in pairs to complete thegraphic organizer. Invite pairs to share theircompleted organizers, and prompt a whole-classcomparative discussion of the previous knowledgeand examples given.fractionExamplesHave students look at the model in problem 2 anddiscuss with a partner ways to remember themeaning of each term. Encourage students to usethe terms numerator and denominator as theydiscuss their thinking.7 equal parts10 equal parts in the whole710···Examples5 of the figure is shaded.6··7 5 7 4 1010···Problem Notes122Students likely understand that fractions arenumbers that express parts of a whole. Studentresponses may include a fraction with labeledparts; a shaded model with labeled parts; or afraction that represents a division expression.A fraction of the model is shaded. What are the numerator and thedenominator of the fraction? Explain how you know.The numerator is 5 because 5 parts of the whole are shaded.The denominator is 8 because the whole circle is divided into8 equal parts.Students should recognize that the shaded partof the model represents the numerator and thenumber of equal parts in the model representsthe denominator.211 Curriculum Associates, LLC Copying is not permitted.LESSON 10 Divide Fractions211REAL-WORLD CONNECTIONFashion designers work with fractions whenthey design and sew clothes. Figuring out howto place buttonholes on the front of a shirtmay require dividing with fractions. Suppose adesigner wants to place 7 buttons on a shirt sothat the distance between the top and bottombuttons is 13 1 inches. The space between the2··buttons can be found by calculating 13 1 4 6.2··Or, suppose a designer wants to put buttons3 1 inches apart so that the distance between4··the top and bottom buttons is 19 1 inches. The2··number of buttons needed can be found bycalculating 19 1 4 3 1 , and then adding 1 to24····the quotient. Ask students to think of otherreal‑word examples where dividing fractionsmight be useful.211LESSON 10 Divide Fractions Curriculum Associates, LLCCopying is not permitted.
LESSON 10 SESSION 1Additional Practice3Problem 3 provides another look at dividing afraction by a whole number. This problem issimilar to the problem about clay animals. Inboth problems, a fraction of a whole is dividedinto smaller parts. This problem asks for theweight of each layer of sand when a fraction ofone pound of sand is divided into smallerequal parts.LESSON 10 SESSION 13Patrick is using layers of colored sand in an art project. He divides 2 lb of3··blue sand into 3 equal parts in order to make 3 layers.a. What is the weight of the sand in each layer of blue sand? Show your work.Possible work:1 of 1 is 1 1 , or 1 .3 ··3 ··39····3··13Students may want to use fraction bars, fractioncircles, grid paper, or number lines to solve.19Suggest that students use Three Reads, askingthemselves one of the following questionseach time: What is this problem about? What is the question I am trying to answer? What information is important?13191919191923SOLUTIONThe weight of the sand in each layer of blue sand is 2 lb.9··b. Check your answer to problem 3a. Show your work.Possible work:If each layer of blue sand weighs 2 lb, then the total weight of 3 layers is3 times 2 . Check by multiplying.9··9··3 2 5 3 29··1··9··5 3 21 9····569··523··So, 2 lb is correct since 3 times 2 equals the starting amount.99····212212LESSON 10 Divide FractionsDIFFERENTIATION ENGLISH LANGUAGE LEARNERS Curriculum Associates, LLC Copying is not permitted.Use with Session 2Apply ItLevels 1–3: Reading/SpeakingLevels 2–4: Reading/SpeakingLevels 3–5: Reading/SpeakingSupport students as they make sense ofApply It problem 8. Read the problem aloud.Use photos or realia to illustrate the meaningof pitcher. Read the first two sentences againand think aloud as you sketch a pitcherlabeled 1 2 L and a larger container labeled5··4 1 L. Read the question. Ask students to5··locate and underline the two expressions. Callon a volunteer to interpret the expressionsusing the sketches and everyday language.Display the expressions and have studentsturn and talk about which expression canbe used to find the number of pitchersSofia can fill. Allow time for students tosolve individually.Support students as they make sense ofApply It problem 8 with Three Reads. Adaptthe routine by displaying sentence starters tohelp students respond in complete sentencesto the questions that correspond with eachreading: The problem is about . . . We are trying to find out . . . The important quantities in the problem are . . . They are related because . . .After each reading, present the question andallow think time for students to formulate aresponse before talking with a partner. Havestudents sketch to show their understandingand solve individually.Support students as they make sense ofApply It problem 8 with Three Reads. Adaptthe routine by having students work in pairsto answer the questions and understand theproblem. Encourage students to speak incomplete sentences when responding to thequestions after each reading. Review withstudents that making a sketch or model canhelp them justify their thinking.Allow time for students to solve the problemindividually, then have them compare andjustify their answers by explaining why itmakes sense given the situation. Curriculum Associates, LLCCopying is not permitted.LESSON 10 Divide Fractions212
LESSON 10 SESSION 2Develop Dividing FractionsPurpose LESSON 10 SESSION 2Develop strategies for dividing fractions (includingmixed numbers) by fractions.Recognize that when dividing by a fraction, anyremainder can be expressed as a fraction of the divisor.JuneteenthFestivalDevelop Dividing Fractions1 Read and try to solve the problem below.STARTCONNECT TO PRIOR KNOWLEDGEImani is planning her city’s Juneteenth festival. There will be3 1 hours of performances on the main stage. Each2··Which Would You Rather?Aperformer’s time slot lasts 3 hour. How many time slots can4··Bofof an appleoffeaturing3 2 Hours ofrmancesPerfofeaturingImani plan to have?of an appleTRYITC E L E B R AT I N G F R E E D O MMath Toolkit fraction bars, fraction circles, grid paper, number linesPossible work:SAMPLE A1 hour 5 60 minutes, and 1 hour 5 30 minutes. Curriculum Associates, LLC Copying is permitted.2··Possible Solutions3 60 1 30 5 210, so there are 210 minutes in 3 1 hours.2··1 hour 5 15 min and 3 15 5 45. So, 3 of an hour is 45 min.44····A because it is the lesser amount, 1 .4··B because it is the greater amount, 3 .4 45 5 180, so at least four 45-min time slots will fit in 210 min.10···210 2 180 5 30, so there are not enough minutes for another time slot.Imani can plan on having 4 time slots that are each 3 hour long.WHY? Support students’ facility withdetermining a fraction of a fraction and preparestudents to think about a remainder as afraction of a fractional divisor.4··SAMPLE B31 4 3 5 ?2··4··34343434DISCUSS IT12Ask: How is yourstrategy similarto mine? How is itdifferent?DEVELOP ACADEMIC LANGUAGE0WHY? Support students as they makeconnections between ideas.HOW? Explain that making connections is aneffective way to deepen understanding of anidea. Display the bar model from Model It andthe division equation from Analyze It. Invitevolunteers to circle parts of the model that arealso represented in the equation and explain theconnection. Provide a sentence frame:connects to because.TRY ITSMP 1, 2, 4, 5, 6Make Sense of the ProblemSee Connect to Culture to support studentengagement. Before students work on Try It, useNotice and Wonder to help them make sense of theproblem. Listen for understanding that the numberof time slots depends on how many 3 -hour timeslots fit into 3 1 hours.1233142You can fit 3 hour into 3 1 hours 4 times, with 1 hour left over.422······The remaining 1 hour is not long enough to make a fifth time slot.2··Imani can plan to have four 3 -hour time slots.4··Share: My strategyis similar to yoursbecause . . . It isdifferent because . . .213LESSON 10 Divide Fractions Curriculum Associates, LLC Copying is not permitted.DISCUSS IT213SMP 2, 3, 6Support Partner DiscussionAfter students work on Try It, encourage them to respond to Discuss It with a partner.If students need support in getting started, prompt them to ask each other questionssuch as: Why did you choose the model or strategy you used? How does your model show 3 1 and 3 ?2··4··Comm
fractions when the fractions were compatible and when the quotient was a whole number. Objectives Content Objectives Divide fractions by fractions using visual models and equations. Use visual models and equations to represent word problems involving fraction division.
10 IXL Practice SOL 6.4: The student will demonstrate multiple representations of multiplication and division of fractions. Multiply fractions: Multiply fractions -with models (Sixth grade V.5) Divide fractions: Divide by fractions -with models (Sixth grade W.1) Divide fractions: Reciprocals (Sixth grade - W.2) SOL 6.6.a: The student will multiply and divide fractions and mixed
Fractions Prerequisite Skill: 3, 4, 5 Prior Math-U-See levels Epsilon Adding Fractions (Lessons 5, 8) Subtracting Fractions (Lesson 5) Multiplying Fractions (Lesson 9) Dividing Fractions (Lesson 10) Simplifying Fractions (Lessons 12, 13) Recording Mixed Numbers as Improper Fractions (Lesson 15) Mixed Numbers (Lessons 17-25)
Adding & Subtracting fractions 28-30 Multiplying Fractions 31-33 Dividing Fractions 34-37 Converting fractions to decimals 38-40 Using your calculator to add, subtract, multiply, divide, reduce fractions and to change fractions to decimals 41-42 DECIMALS 43 Comparing Decimals to fractions 44-46 Reading & Writing Decimals 47-49
Year 5 is the first time children explore improper fractions in depth so we have added a recap step from Year 4 where children add fractions to a total greater than one whole. What is a fraction? Equivalent fractions (1) Equivalent fractions Fractions greater than 1 Improper fractions to mix
fractions so they have the same denominator. You can use the least common multiple of the denominators of the fractions to rewrite the fractions. Add _8 15 1 _ 6. Write the sum in simplest form. Rewrite the fractions as equivalent fractions. Use the LCM as the denominator of both fractions
(a) Fractions (b) Proper, improper fractions and mixed numbers (c) Conversion of improper fractions to mixed numbers and vice versa (d) Comparing fractions (e) Operations on fractions (f) Order of operations on fractions (g) Word problems involving fractions in real life situations. 42
Decimals to Fractions (Calculator) [MF8.13] Ordering Fractions, Decimals and Percentages 1: Unit Fractions (Non-Calculator) [MF8.14] Ordering Fractions, Decimals and Percentages 2: Non-Unit Fractions (Non-Calculator) [MF8.15] Ordering Fractions, Decimals and Percentages 3: Numbers Less than 1 (Calculator) [MF8.16] Ordering Fractions, Decimals .
Astrology: The alignment of the planets and stars was very important, looking at when the patient was born and fell ill to decide what was wrong with them! This became more popular after the Black Death (1348) Astrology is a SUPERNATURAL explanation for disease. Apothecaries mixed ingredients to make ointments and medicines for the physicians. They learned from other apothecaries. They also .
